Zuowei Liu Nanjing University - icts.ustc.edu.cn

Probingmillicharge@electroncolliders

ZuoweiLiu

NanjingUniversity

UniversityofScienceandTechnologyofChinaMarch25,2021

1

Millichargeisaverysmallelectriccharge

e Qf Aγμ f̄ γμ f

photon

2


u c t

d s b

νe νμ ντ

e μ τ

γ

g

Z

H

W

e Qf Aγμ f̄ γμ f

photon

2


u c t

d s b

νe νμ ντ

e μ τ

γ

g

Z

H

W

Q = 0e Qf Aγ

μ f̄ γμ f

photon

2


u c t

d s b

νe νμ ντ

e μ τ

γ

g

Z

H

W

Q =23

Q = − 1

Q = −13

Q = 0e Qf Aγ

μ f̄ γμ f

photon

2


u c t

d s b

νe νμ ντ

e μ τ

γ

g

Z

H

W

Q =23

Q = − 1

Q = −13

Q = 0e Qf Aγ

μ f̄ γμ f

is quantized in SMQf =n3

photon

2


u c t

d s b

νe νμ ντ

e μ τ

γ

g

Z

H

W

Q =23

Q = − 1

Q = −13

Q = 0e Qf Aγ

μ f̄ γμ f

is quantized in SMQf =n3

non-quantized Qf ≡ ϵ ≪ 1 millicharge

photon

2

Magneticmonopoleleadstochargequantization

[fromh<ps://inspirehep.net/]

Dirac’spaperonmagneFcmonopole&chargequanFzaFonin1931

3

Magneticmonopoleleadstochargequantization

[fromh<ps://inspirehep.net/]

e =2πℏn

μmagneFcmonopole

chargequanFzaFon

ismagneFcstrengthμ

iselectricstrengthe

isintegern

Dirac’spaperonmagneFcmonopole&chargequanFzaFonin1931

3

Standardmodel&grandunifiedtheories

“chargequanFzaFon”isnotresolvedcompletelyinSM

SU(3)c × SU(2)L × U(1)Y

4

Standardmodel&grandunifiedtheories

“chargequanFzaFon”isnotresolvedcompletelyinSM

SU(3)c × SU(2)L × U(1)Y

Embeddedintoabiggergaugegroup,e.g.SU(5) [Georgi&Glashow,PRL.32.438,1974]

chargequanFzaFon

4

StringentconstraintsonmillichargeinSM

[Marinellietal.1984]

[Bressietal.2011]

[Baumannetal.1988]

[Barbiellinietal.1987]

Qp − Qe < (0.8 ± 0.8) × 10−21e

Qn < (−0.1 ± 1.1) × 10−21e

Qn < (−0.4 ± 1.1) × 10−21e

Qν < 10−17e

[Siemensenetal.,PRD97,052004(2018)]

5

MillichargeinBSMcanbequite“large”

[Jaeckel&Ringwald,1002.0329] e ϵ Aγμ χ̄ γμ χ

log10(mχ /eV)

log 1

0(ϵ)

6



log10(mχ /eV)

log 1

0(ϵ)

astro/cosmo6

log 1

0(ϵ)

log10(mχ /eV)



log10(mχ /eV)

log 1

0(ϵ)

significant allowedϵ

astro/cosmo6

log 1

0(ϵ)

log10(mχ /eV)

Probingmillichargeatelectroncolliders

7

log 1

0(ϵ)

log10(mχ /eV)


0.1-10GeV

accessibleatelectroncolliders

BaBarBESIIIBelleIISTCF

7

MillichargedDMexplainsEDGES21cmanomaly

[EDGES2018]

8


coldergasorhoYerCMBthanexpected

[EDGES2018]

8


coldergasorhoYerCMBthanexpected

[EDGES2018]

MillichargedDMxsec

σ ∝ v−4

easiertoevadeearlyuniverseconstraints

DMcancoolgas

8

Outline:discussionsonmillicharge

[Feldman,ZL,Nath,hep-ph/0702123,299cites]

1 theoreFcalmodels

2 terrestrialsearches

3 electroncolliders’sensiFvity[ZL,Zhang,1808.00983]

[Liang,ZL,Ma,Zhang,1909.06847]

9

1 theoreFcalmodels


10

Modelstogeneratemillichargedparticles(MCPs)


KineFcmixing

Massmixing

e ϵ Aγμ χ̄ γμ χ is MCPχ

11

KineticmixingbetweentwoU(1)fields

ℒ = −14

F2μνFμν2 −

δ2

F2μνFμν1 −

14

F1μνFμν1

KineFcmixingbetweentwoU(1)fields: &A1 A2

[Foot&He,Phys.Le<.267B,509(1991)]

12

[Holdom,Phys.Le<.166B,196(1986)]


ℒ = −14

F2μνFμν2 −

δ2

F2μνFμν1 −

14

F1μνFμν1


[Foot&He,Phys.Le<.267B,509(1991)]

δ

e−

e+

γ γ′

χ̄

χ

standardmodel

hiddensector

12



ℒ = −14

F2μνFμν2 −

δ2

F2μνFμν1 −

14

F1μνFμν1


[Foot&He,Phys.Le<.267B,509(1991)]

δ

e−

e+

γ γ′

χ̄

χ

standardmodel

hiddensector

12

millicharge ∼ δ


Oneexampletogeneratekineticmixing

2highscalefermionschargedundertwoU(1)s

[Holdom,Phys.Le<.166B(1986)196-198]

13

Oneexampletogeneratekineticmixing

2highscalefermionschargedundertwoU(1)s

[Holdom,Phys.Le<.166B(1986)196-198]

ℒ = −14

F2μνFμν2 −

14

F1μνFμν1 −

δ2

F2μνFμν1

δ =e1e2

6π2ln

m′ 12

m12

13

Modelstogeneratemillichargedparticles(MCPs)

KineFcmixing

Massmixing

14

StueckelbergmassmixingbetweentwoU(1)fields

ℒ = −14

F2μνFμν2 −

12

(∂μσ + M1A1μ + M2A2μ)2 −14

F1μνFμν1

StueckelbergmassmixingbetweentwoU(1)fields: &A1 A2[Kors&Nathhep-ph/0402047]

[Cheung&Yuanhep-ph/0701107][Feldman,ZL,Nath,hep-ph/0603039]

15


ℒ = −14

F2μνFμν2 −

12

(∂μσ + M1A1μ + M2A2μ)2 −14

F1μνFμν1


ϵ

e−

e+

γ γ′

χ̄

χ

standardmodel

hiddensector

ϵ ∼M2

M1≪ 1


15


ℒ = −14

F2μνFμν2 −

12

(∂μσ + M1A1μ + M2A2μ)2 −14

F1μνFμν1


ϵ

e−

e+

γ γ′

χ̄

χ

standardmodel

hiddensector

ϵ ∼M2

M1≪ 1


15

millicharge ∼ ϵ

“Toy”modelw/bothkinetic&massmixings

−14

F1μνFμν1 −

14

F2μνFμν2 −

δ2

F1μνFμν2 +J′ μAμ

1 +JμAμ2 −

12

M21 A1μAμ

1 −12

M21ϵ2A2μAμ

2 −M21ϵA1μAμ

2


16

[Fabbrichesietal.,2005.01515,TheDarkPhoton,p7-9]


−14

F1μνFμν1 −

14

F2μνFμν2 −

δ2


1 +JμAμ2 −

12

M21 A1μAμ

1 −12

M21ϵ2A2μAμ

2 −M21ϵA1μAμ

2


1

1 − 2δϵ + ϵ2 ( ϵ − δ

1 − δ2Jμ+

1 − δϵ

1 − δ2J′ μ) Aμ

M +1

1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ

a_erfieldredefiniFon&rotaFon canonical &diagonalmassmatrix⟶ (−F2/4)

16



−14

F1μνFμν1 −

14

F2μνFμν2 −

δ2


1 +JμAμ2 −

12

M21 A1μAμ

1 −12

M21ϵ2A2μAμ

2 −M21ϵA1μAμ

2


1

1 − 2δϵ + ϵ2 ( ϵ − δ

1 − δ2Jμ+

1 − δϵ

1 − δ2J′ μ) Aμ

M +1

1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ


SM photon

16



−14

F1μνFμν1 −

14

F2μνFμν2 −

δ2


1 +JμAμ2 −

12

M21 A1μAμ

1 −12

M21ϵ2A2μAμ

2 −M21ϵA1μAμ

2


1

1 − 2δϵ + ϵ2 ( ϵ − δ

1 − δ2Jμ+

1 − δϵ

1 − δ2J′ μ) Aμ

M +1

1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ


dark photon SM photon

16



−14

F1μνFμν1 −

14

F2μνFμν2 −

δ2


1 +JμAμ2 −

12

M21 A1μAμ

1 −12

M21ϵ2A2μAμ

2 −M21ϵA1μAμ

2


1

1 − 2δϵ + ϵ2 ( ϵ − δ

1 − δ2Jμ+

1 − δϵ

1 − δ2J′ μ) Aμ

M +1

1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ


degeneracy dark photon SM photon

16



−14

F1μνFμν1 −

14

F2μνFμν2 −

δ2


1 +JμAμ2 −

12

M21 A1μAμ

1 −12

M21ϵ2A2μAμ

2 −M21ϵA1μAμ

2


1

1 − 2δϵ + ϵ2 ( ϵ − δ

1 − δ2Jμ+

1 − δϵ

1 − δ2J′ μ) Aμ

M +1

1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ


degeneracy dark photon SM photon

mass mixing millicharge→

16


“Realistic”modelw/bothkinetic&massmixings


17

commonfeatures

hiddenbosonmixw/hypercharge(insteadofphoton)

hiddenbosonphoton-like(darkphoton)

hypercharge-like mA′ ≫ mZ

mA′ ≪ mZ

3by3massmatrix⟹

“Realistic”modelw/bothkinetic&massmixings


17

commonfeatures

hiddenbosonmixw/hypercharge(insteadofphoton)

hiddenbosonphoton-like(darkphoton)

hypercharge-like mA′ ≫ mZ

mA′ ≪ mZ

3by3massmatrix⟹

kineFcmixing millicharge&masslessdarkphoton⟹massmixing millicharge&massivedarkphoton⟹

difference

2 terrestrialsearches

18

Twowaysto“detect”millichargedparticles

scinFllaFon/ionizaFon/scaYering

missingenergy

e ϵ Aγμ χ̄ γμ χ is MCPχ

[ZL,Zhang,1808.00983]

[Liang,ZL,Ma,Zhang,1909.06847]19

SLACmQ:electronbeamdumpexperiment

[Prinzetal,PRL81.1175,1998]

20


electron beam


20


electron beam

sandstone


20


electron beam

sandstone


ordinary charged particles < 90 m

20


electron beam

sandstone

scintillation counter


ordinary charged particles < 90 m

20

SLACmQconstraintsonmillicharge


21

SLACmQconstraintsonmillicharge


m>100MeVMCPyielddieoff

21

MilliQan:proposedscintillationdetector@LHC

[Haasetal.,1410.6816]

22

[Balletal.,1607.04669]

MilliQan:proposedscintillationdetector@LHC

[Haasetal.,1410.6816]plasFc

scinFllatorsarraywith3secFons(poinFngtoCMSIP),each

containing400

scinFllatorbarscoupledtoPMT.33mawayfromCMSIP.

1 m × 1 m × 3 m

5 cm × 5 cm × 80 cm

22

[Balletal.,1607.04669]

MilliQansensitivityonmillichargedparticles

[Balletal.,1607.04669]

23

MilliQansensitivityonmillichargedparticles

[Balletal.,1607.04669]

photoelectrondropsbelowonewhen

ϵ ≲ O(10−3)

23

ArgoNeuT@FermiLab:liquidargoneutrinodetector

[Harniketal.,1902.03246]

24

[ArgoNeuT,1911.07996]



NuMI target

24

[ArgoNeuT,1911.07996]



NuMI targetLiquid argon time

projection chamber

24

[ArgoNeuT,1911.07996]

LimitsfromArgoNeuT&MilliQandemonstrator(1%)

[ArgoNeuT,1911.07996]

ArgoNeuT POT1020

25

LimitsfromArgoNeuT&MilliQandemonstrator(1%)

[milliQandemonstrator,2005.06518]

1%oftotaldetector

37/iin2018

[ArgoNeuT,1911.07996]

ArgoNeuT POT1020

25

MCPscattersw/neutrinoexperimenttarget

MCP produced in proton fixed-target experiments

MCP scatters w/ target (electron) in the neutrino detector

[Magilletal.,1806.03310]

solid:datadashed:projecFon

26

Somefutureexperimentsonmillicharge(incomplete)

LDMX:electronfixedtarget

FerMINI:scinFllators@protonfixedtarget

NA64:muonfixedtarget

SUBMET:scinFllators@JPARC

neutrinoexperiments

DMexperiments

27

3 electroncolliders’sensiFvity

[ZL,Zhang,1808.00983]

[Liang,ZL,Ma,Zhang,1909.06847]

28

log 1

0(ϵ)

log10(mχ /eV)


0.1-10GeV



[ZL,Zhang,1808.00983][Liang,ZL,Ma,Zhang,1909.06847]

29

log 1

0(ϵ)

log10(mχ /eV)


0.1-10GeV




inabilityofthedetectors

missingenergy

29

Processtosearchformillichargedparticles

verysmallionizaFonsignalfrommillicharge

mono-photon@electroncolliders

[ZL,Zhang,1808.00983]

30




e−

e+

e

γ

χ̄

χ

γ

γ

[ZL,Zhang,1808.00983]

30




e−

e+

e

γ

χ̄

χ

γ

γ

[ZL,Zhang,1808.00983]

millicharge vertex: e ϵ Aγμ χ̄ γμ χ

30




e−

e+

e

γ

χ̄

χ

γ

γ

[ZL,Zhang,1808.00983]


“invisible”atelectroncolliders

30




e−

e+

e

γ

χ̄

χ

γ

γ

[ZL,Zhang,1808.00983]


monophoton

“invisible”atelectroncolliders

30

IrreducibleBG(monophotonplus2neutrinos)

e

e

νν

γe

Z

e

e

νe

νe

γ

W

e

e

e

νe

νe

γ

W

W

IrreducibleBG:e+e− → γνν

31

IrreducibleBG(monophotonplus2neutrinos)

e

e

νν

γe

Z

e

e

νe

νe

γ

W

e

e

e

νe

νe

γ

W

W

small

IrreducibleBG:e+e− → γνν

31

monophotoncrosssection@electroncolliders

millichargeprocess:e+e-→𝞆𝞆ɣ

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[ZL,Zhang,1808.00983]

32

monophotoncrosssection@electroncolliders

millichargeprocess:e+e-→𝞆𝞆ɣ

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1/2<latexit sha1_base64="hxTRVKmJATh5x2QtM/HKdhDyxDI=">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</latexit><latexit sha1_base64="hxTRVKmJATh5x2QtM/HKdhDyxDI=">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</latexit><latexit sha1_base64="hxTRVKmJATh5x2QtM/HKdhDyxDI=">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</latexit><latexit sha1_base64="hxTRVKmJATh5x2QtM/HKdhDyxDI=">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</latexit>

[ZL,Zhang,1808.00983]

irreducibleBG:e+e-→ɣνν

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#

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f(sW ) = 8s4W � 4s2W /3 + 1<latexit sha1_base64="JHyVl0+zIkoW6by+g9sTDA266Ao=">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</latexit><latexit sha1_base64="JHyVl0+zIkoW6by+g9sTDA266Ao=">AAAGd3icdVRbb9MwFPYGK6PcNnhECItuMITYmjKJCQlpl5eJpyFt7bSmVLZz0oY5F2xnW2vliV/DK/wafgpvOGnUNUlrKdHR933n+JzjY9OIe1I1m3+Xlu/cXandW71ff/Dw0eMna+tP2zKMBYMzFvJQnFMigXsBnClPcTiPBBCfcujQy6OU71yBkF4YnKpRBD2fDALP9RhRBuqvvXC3ZL/zFn/Ge9gY33bf493MaO18eGf11xrN7Wa2cNWwcqOB8nXSX185tJ2QxT4EinEiZddqRqqniVAe45DU7VhCRNglGUDXmAHxQfZ0VkeCNw3iYDcU5gsUztBZD018KUc+NUqfqKEscyk4j+vGyt3raS+IYgUBm2zkxhyrEKdNwY4ngCk+MgZhwjO5YjYkgjBlWle3A7hmoe+TwNH2mCZdq6e1nWWnKY8h0Q0rSZKSThR0ApypbCYx1wsI7+mBINHQYzdJfdO58iLH9eeWVgAp9ZOyKm2brKBZywogJwpuDFxEb7OYTRGCgZnDYU9TQoEXPfyYK0+E10XU5SFRRSgWJU9phmNoelIAbyZzUMCG5nyEADep120HXFtybXNOIr2xs5EkmznomrNqWI2W6bepTEk14mDabYdm9nGjVTkdag7N/AZeoOFHnN2FsgRSCRhrkYCSaQwiBBlVApA8wFyWAplJIZgfYRpikUJKaRTSzGyk8n9aulEJmNWZ4bPTERK+dsoxHFPohKUuhgSX6MiZoaMK7RzP0McV+jurXIMvR5/wvBujRBpJ+NgYJep0MTVoJ3rQzzqB2xXy4JY8KJOsk2iWk51KYw0pF5FsnHraY1Ck7DZO3eYyF2kJabiLyl4X0ZR7Y0jz6lrlN7ZqtFvbVnPb+rrb2D/M399V9By9QlvIQh/RPjpGJ+gMMfQT/UK/0Z+Vf7WXtde1rYl0eSn3eYYKq2b9B/IuV1g=</latexit><latexit sha1_base64="JHyVl0+zIkoW6by+g9sTDA266Ao=">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</latexit><latexit sha1_base64="JHyVl0+zIkoW6by+g9sTDA266Ao=">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</latexit>

sW ⌘ sin ✓W<latexit sha1_base64="F3b5vGIN378EI0G8l9YZeRCNX40=">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</latexit><latexit sha1_base64="F3b5vGIN378EI0G8l9YZeRCNX40=">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</latexit><latexit sha1_base64="F3b5vGIN378EI0G8l9YZeRCNX40=">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</latexit><latexit sha1_base64="F3b5vGIN378EI0G8l9YZeRCNX40=">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</latexit>

[Ma,Okada1978]

[Gaemers+1979]

32

“Low”collidingenergyisbettertoprobeMCPs

2 4 6 8 10 12 14ps (GeV)

10°2

10°1

100

101

102æ

(fb)

Pre-selection Cuts≤ = 0.001

m¬ = 0.1 GeV

irreducible SM BG

ifirreducibleBGistheonlyimportantBG

33


2 4 6 8 10 12 14ps (GeV)

10°2

10°1

100

101

102æ

(fb)


m¬ = 0.1 GeV

irreducible SM BG

e+e− → γ χ̄ χ


33


2 4 6 8 10 12 14ps (GeV)

10°2

10°1

100

101

102æ

(fb)


m¬ = 0.1 GeV

irreducible SM BG

e+e− → γ χ̄ χ

e+e− → γ ν̄ ν


33

BelleIIhasseveraluncoveredangularregions

7GeVelectroncollidesw/4GeVpositron

35



[BelleII1808.10567]

ECLangles(labframe)

12.4∘ < θ < 31.4∘

32.2∘ < θ < 128.7∘

130.7∘ < θ < 155.1∘

35



reducibleBGBGduetoECLgaps(gBG)

BGduetobeam(bBG)

[BelleII1808.10567]

ECLangles(labframe)

12.4∘ < θ < 31.4∘

32.2∘ < θ < 128.7∘

130.7∘ < θ < 155.1∘

35

Dark Sectors at Low Energy Colliders (Torben Ferber) �22

Background MC, 40 fb-1 after selection

ee→eeγboth electrons

out of tracking acceptance

ee→2γ and 3γ 1γ in ECL 90° gap

1γ out of ECL acceptance

ee→2γ 1γ in ECL BWD or FWD gap

ee→3γ 1γ in ECL BWD gap

1γ out of ECL acceptance

Belle II MC

Introduction• Dark Photon A’ motivated by Dark Matter, g-2, ..

• Minimal Dark Matter model: Dark Matter particle χ and a new scalar or gauge Boson A’ as s-channel annihilation mediator (mA’ > 2mχ)

• Additional U(1)’ symmetry → Kinetic mixing* of massive Dark Photon with the SM photon

313/28

Towards First Physics: Dark Photon.

>Dark Photon motivated by dark matter, g-2 anomaly...

>Minimal dark matter model: Dark matter particle N and a new scalar or gauge boson A' as s-channel annihilation mediator (mA' > 2mN)

>Additional U(1)' symmetry ? “Kinetic Mixing”* of massive dark photon A' with the SM photon

*Holdom, Phys. Lett B166, 1986

Eγ=s−M A'

2

2√ s

13/28

Towards First Physics: Dark Photon.

>Dark Photon motivated by dark matter, g-2 anomaly...

>Minimal dark matter model: Dark matter particle N and a new scalar or gauge boson A' as s-channel annihilation mediator (mA' > 2mN)

>Additional U(1)' symmetry ? “Kinetic Mixing”* of massive dark photon A' with the SM photon

*Holdom, Phys. Lett B166, 1986

Eγ=s−M A'

2

2√ s

B: Invisible Dark Photon searches

Belle

[takenfromTorbenFerber’stalk]

36

20 40 60 80 100 120 140µ∞

lab (deg)

2

3

4

5

6

E∞ cm

(GeV

)

high-mass

low-massbBG

Belle II

Photonenergyandangularcuts@BelleII

[Liang,Liu,Ma,Zhang,1909.06847]37

20 40 60 80 100 120 140µ∞

lab (deg)

2

3

4

5

6

E∞ cm

(GeV

)

high-mass

low-massbBG

Belle II


bBG


20 40 60 80 100 120 140µ∞

lab (deg)

2

3

4

5

6

E∞ cm

(GeV

)

high-mass

low-massbBG

Belle II


bBG

lowmassregion

[BelleII1808.10567]


20 40 60 80 100 120 140µ∞

lab (deg)

2

3

4

5

6

E∞ cm

(GeV

)

high-mass

low-massbBG

Belle II


bBG

lowmassregion

[BelleII1808.10567]

[Liang,Liu,Ma,Zhang,1909.06847]

highmassregion

[BelleII1808.10567]

37

electroncollidersprobenewparameterregion(95%CL)

0.001 0.01 0.1 1 4m¬ (GeV)

10°5

10°4

10°3

10°2

10°1

"

Colliders

BaBar 28/fb

BESIII 17/fbBelle II 50/ab

STCF 20/ab

SLAC

√MiniBooNE

√LSND

CMB

ann.

fdm= 10

°2

fdm= 10

°3

ArgoNeuT

NeÆ

Belle II bBG+gBG

Belle II bBG

Belle II optimized

BESIII bBG

STCF bBG

STCF optimized



0.001 0.01 0.1 1 4m¬ (GeV)

10°5

10°4

10°3

10°2

10°1

"

Colliders

BaBar 28/fb


STCF 20/ab

SLAC

√MiniBooNE

√LSND

CMB

ann.

fdm= 10

°2

fdm= 10

°3

ArgoNeuT

NeÆ

Belle II bBG+gBG

Belle II bBG

Belle II optimized

BESIII bBG

STCF bBG

STCF optimized


BaBar

38


0.001 0.01 0.1 1 4m¬ (GeV)

10°5

10°4

10°3

10°2

10°1

"

Colliders

BaBar 28/fb


STCF 20/ab

SLAC

√MiniBooNE

√LSND

CMB

ann.

fdm= 10

°2

fdm= 10

°3

ArgoNeuT

NeÆ

Belle II bBG+gBG

Belle II bBG

Belle II optimized

BESIII bBG

STCF bBG

STCF optimized


BaBar

BESIII

38


0.001 0.01 0.1 1 4m¬ (GeV)

10°5

10°4

10°3

10°2

10°1

"

Colliders

BaBar 28/fb


STCF 20/ab

SLAC

√MiniBooNE

√LSND

CMB

ann.

fdm= 10

°2

fdm= 10

°3

ArgoNeuT

NeÆ

Belle II bBG+gBG

Belle II bBG

Belle II optimized

BESIII bBG

STCF bBG

STCF optimized


BaBar

BESIII

BelleII

38


0.001 0.01 0.1 1 4m¬ (GeV)

10°5

10°4

10°3

10°2

10°1

"

Colliders

BaBar 28/fb


STCF 20/ab

SLAC

√MiniBooNE

√LSND

CMB

ann.

fdm= 10

°2

fdm= 10

°3

ArgoNeuT

NeÆ

Belle II bBG+gBG

Belle II bBG

Belle II optimized

BESIII bBG

STCF bBG

STCF optimized


BaBar

BESIII

BelleII

STCF

38


0.001 0.01 0.1 1 4m¬ (GeV)

10°5

10°4

10°3

10°2

10°1

"

Colliders

BaBar 28/fb


STCF 20/ab

SLAC

√MiniBooNE

√LSND

CMB

ann.

fdm= 10

°2

fdm= 10

°3

ArgoNeuT

NeÆ

Belle II bBG+gBG

Belle II bBG

Belle II optimized

BESIII bBG

STCF bBG

STCF optimized


BaBar

BESIII

BelleII

STCF

diffBGconsideraFons

38


0.001 0.01 0.1 1 4m¬ (GeV)

10°5

10°4

10°3

10°2

10°1

"

Colliders

BaBar 28/fb


STCF 20/ab

SLAC

√MiniBooNE

√LSND

CMB

ann.

fdm= 10

°2

fdm= 10

°3

ArgoNeuT

NeÆ

Belle II bBG+gBG

Belle II bBG

Belle II optimized

BESIII bBG

STCF bBG

STCF optimized


BaBar

BESIII

BelleII

STCF

diffBGconsideraFons

newregions:0.1-4GeV

38


0.001 0.01 0.1 1 4m¬ (GeV)

10°5

10°4

10°3

10°2

10°1

"

Colliders

BaBar 28/fb


STCF 20/ab

SLAC

√MiniBooNE

√LSND

CMB

ann.

fdm= 10

°2

fdm= 10

°3

ArgoNeuT

NeÆ

Belle II bBG+gBG

Belle II bBG

Belle II optimized

BESIII bBG

STCF bBG

STCF optimized


BaBar

BESIII

BelleII

STCF

diffBGconsideraFons

?ϵ ≲ O(10−4)

newregions:0.1-4GeV

38

Summary

MillichargedparFclescanappearinkineFcmixingorStueckelbergmassmixingmodels

AnumberofterrestrialexperimentshavebeencarriedoutorproposedtosearchformillichargedparFcles

WeproposetosearchformillichargedparFclesatelectroncolliders,includingBESIII,Belle-IIandSTCF,whichcanprobecurrentlyunexploredparameterregions:ϵ ≲ O(10−3) for 100 MeV ≲ m ≲ several GeV

39



addiFonalslides

40

0.001 0.01 0.10 1 3m¬ (GeV)

10°5

10°4

10°3

"

7 GeV

4 GeV

2 GeV STCF 10/ab

DifferentSTCFcollidingenergies

STCFlow-Emode:beYerforlowmass

41

0.01 0.10 1 5m¬ (GeV)

10°1

100"

High-E

Low-E

BaBar 28/fb

BaBarsensisvityonmillicharge

[BaBar,0808.0017]

High-E3.2 < E⇤

� < 5.5 GeV<latexit sha1_base64="11o7ygJIXiln6j5YnuV4AV0tbUA=">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</latexit>

�0.31 < cos ✓⇤� < 0.6<latexit sha1_base64="U70maJk/dG0auGOVbGqAKupCVAU=">AAAGinicdVRdb9MwFPUGK6MM2OCRF4tuAiFRkg7xuYd98DDxNKStndaUynGcNMz5wHa2tZb/Br+GV/gP/Btu2qprkjZSoqtzzr25Pr62m/JQKsv6t7J65+5a7d76/fqDjYePHm9uPWnLJBOUndGEJ+LcJZLxMGZnKlScnaeCkcjlrONeHuV854oJGSbxqRqmrBeRIA79kBIFUH/TcsY1tMszZvRrq7lr72HApKMGTJHv+pXpOwGJIoL3sNV8Z/qbDatpjR9cDexp0EDT56S/tXboeAnNIhYryomUXdtKVU8ToULKmak7mWQpoZckYF0IYxIx2dPjtgzeAcTDfiLgjRUeo/MZmkRSDiMXlBFRA1nmcnAR182U/6GnwzjNFIvp5Ed+xrFKcO4T9kLBqOJDCAgVIfSK6YAIQhW4WXdidk0TcCX2tDNyTdfuaV2wsmEbY0o6UdAJ5s1kc435YUx4TweCpIOQ3pj6jncVpp4fLVxaAXTdyJRVuW2ygo4tK4CcKHYDcBG97WK+RRYHMJqDnnaJy3gxI8q4CkVyXUR9nhBVhDJRypQwHAPwpADeTOaggA1gf4RgvqnXHY/5juTa4ZykevvNtjE7U9CHvWrYjRb4DStTUg05A7udBI4DbrQqu+PCpsEnCGPNfmbj41GWsFzCIFomcMmsBhGCDCsFyLTAQtZlZK6FeHGFWYllCiklKCTMbKqm33zpoBJsXgfD5+QjJCLtlWt4sNAJ6/qYGVyiU2+OTiu0dzxHH1foH7RyDL4efcKLTowSeSURYQhK1OlyKmgbHfTHTuB2hTy4JQ/KJO0YTadkp2IskHIZSUd5pjOCO7OcNsrTFjIX+RLycheVf12kM+4FkHDr2uU7thq0W017t2l9e9vYP5zev+voGXqOXiIbvUf76BidoDNE0S/0G/1Bf2sbtVbtY+3zRLq6Ms15igpP7ct//NlgUA==</latexit>

Low-E2.2 < E⇤

� < 3.7 GeV<latexit sha1_base64="pVADkRPFC44zF9JHX0gDI8gP0yI=">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</latexit>

�0.46 < cos ✓⇤� < 0.46<latexit sha1_base64="HzSE/my43Ds/lV8GU2ebkyOC2RA=">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</latexit>

high-EdatahasbeYersensiFvitytolightmass42

MassgrowthviaStueckelberg

MakemassiveQEDgaugeinvariantbyaddingaxion𝞂

L = �1

4Fµ⌫F

µ⌫ � m2

2A2

µ

=) � 1

4Fµ⌫F

µ⌫ � 1

2(mAµ + @µ�)

2

<latexit sha1_base64="YFG7yL3iWuVFtFI4jeywUNVL3yU=">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</latexit><latexit sha1_base64="YFG7yL3iWuVFtFI4jeywUNVL3yU=">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</latexit><latexit sha1_base64="YFG7yL3iWuVFtFI4jeywUNVL3yU=">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</latexit><latexit sha1_base64="YFG7yL3iWuVFtFI4jeywUNVL3yU=">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</latexit>

�Aµ = @µ�, �� = �m�

invariantundergaugetransformaFon

σ:longitudinalmodeofthevectorboson

[E.C.G.Stueckelberg,Helv.Phys.Acta11,225(1938)]43

Stueckelberginextradimensions

compacFficaFonofa5Dtheoryonhalf-circle

L5 = �1

4Fab(z)F

ab(z), a, b = 0, 1, 2, 3, 5

infinitenumberofmassiveKKmodesin4D

�1

2

X

n

M2n

✓A(n)

µ (x) +1

Mn@µ�

(n)(x)

◆2

L4 = �1

4

X

n

F (n)µ⌫ (x)Fµ⌫(n)(x)

Stueckelbergmassin4DduetocompacFficaFon[Nath0812.0958]

S1/Z2

za = (xµ, y), µ = 0, 1, 2, 3 Aa = (Aµ(z),�(z))

44

StueckelbergvsHiggsU(1)bosonw/aHiggspotenFal

L = �1

4Fµ⌫F

µ⌫ +h(@µ + igAµ)�

i2�

hµ2�⇤�+ �(�⇤�)2

i

DecomposetheHiggsfieldinpolarcoordinates

� =

✓v + hp

2

◆ei

�v v =

r�µ2

�

Unitarygauge �U =v + hp

2

L = �F 2U

4+

(@µh)2

2+

g2

2(h+ v)2AU

µAUµ � �

4(h2 + 2hv)2 +

�

4v4

AUµ = Aµ � 1

gv@µ�&

Mh =p2�v

<latexit sha1_base64="xSzQrbMn6Jwcub2yhTe7GH6zB8E=">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</latexit>

MA = gv<latexit sha1_base64="kdcqK2k4uqbklQvoxKC/zJOOXyI=">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</latexit>

𝛔disappears45

decoupletheHiggsparticle

L = �F 2U

4+

M2A

2AU

µAUµ

AUµ = Aµ � 1

MA@µ�

LowenergyeffecFvetheory

L = �F 2µ⌫

4+

1

2(MAAµ � @µ�)

2

TheHiggsmechanismleadstotheStueckelbergmechanism.

[Allen,Bowick,Lahiri,Mod.Phys.Le<.A6,559,(1991)][Nath,arXiv:0812.0958] [Nelson,Scholtz,arXiv:1105.2812]

Take the limits �µ2 ! 1, � ! 1 with v =

p�µ2/� fixed.

In this case, the Higgs field Mh =p2�v becomes infinitely

heavy and decouples, whereas the gauge boson mass

MA = gv remains unchanged.

46

Zuowei Liu Nanjing University - icts.ustc.edu.cn

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